Area of a circle (lets all it Ac) is [pi]r^2
Circumference of a circle, c, is 2[pi]r
Therefore the area of a circle, with respect to circumference is:
Ac = 4[pi]^3 / c^2
We know that the area of a square (lets call it As) is x^2, where x is the length of a side
Ac = As as per the question, so:
4[pi]^3 / c^2 = x^2
we also know that c + 4x = 1 meter
Which can be arranged as
c = 1 - 4x
We now have 2 equations with 2 unknowns, just substitute the 'c'
4[pi]^3 / (1 - 4x)^2 = x^2
The numbers in this are horrible....
I'll leave it at that stage (tired!)
But that's how you go about solving these types of question.